Lecture 13 - Addition of Angular Momentum and spin Total...

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Addition of Angular Momentum and spin
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Total angular momentum Let’s consider states, in which a particle has both angular momentum and spin. Can we define something like total angular momentum? In order to define this operator, which can symbolically written as 0 ; 0 lm lm lm lm lm ψ = ↑ = = = + J L S We first of all need to understand the structure of states on which this operator acts. Consider, for instance states, in which orbital momentum and its z-component have definite values. For each of such a state there are two spin states, in which z-component of the spin operator has a definite value. We can consider action of this operator on the states which are two dimensional column states of the form The inner product of these states is defined by treating orbital and spin coordinates separately. This definition conforms to the idea that as these states are mutually exclusive, they must be orthogonal. ( 29 ( 29 1 1 1 2 2 2 1 1 2 2 1 2 2 2 1 1 1 1 2 2 1 1 2 2 , , 0 0 ; 0 0 0 l m s l m s l m l m s s l m l m l m l m l m l m = = =
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This note was uploaded on 09/27/2010 for the course PHYSICS 365 taught by Professor Deych during the Spring '10 term at SUNY Stony Brook.

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Lecture 13 - Addition of Angular Momentum and spin Total...

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